Is there a way to make a hair particle look like a mesh I've already made?
There are a few add-ons like Hair Net that can generate and hair particles to follow a given curve, fibers (converted curves, just edges), or sheets (hair cards).
Have a look here: How can I merge this Head and Body models?
Hair cards, as used for game characters, can be used directly for the add-ons.
If you have sculpted hair you can layout Bezier-Curves on the surface of it. Just activate the snapping tool. 
After you have done a complete layer of curves, duplicate the curves 2 or 3 times, scale and move them a little. Don't forget to Apply Scale and Location (Ctrl+A in Object Mode) for the curves and the head (emitter) when you're done with the layout. That's important.
Finally, generate the Hair Particle System. Select the Curve objects first, then the head/scalp object (emitter). The emitter selection must be orange, the curve selection must be red.

Sculpted hair (purple), curves (black), duplicated curves, finally the generated hair particles (green)
In the Hair Net add-on in the N-panel, select a Hair Setting (optional) and press the &quot;Curves&quot; button. The script may run a while.
Switch Children type to Simple and give it a tiny bit of Roughness and Randomness in the Hair Particle settings. Use a small value (like 0.02 m) for Radius of the children.
Hair grooming takes a bit of practice. Try to do the hair layered, and don't let the hair guides intersect. That can look messy if you activate the hair children. Make sure you have your model on a real-world scale and adjust values of the Hair Shape. (Shape: -0.850, Diameter root: 0.03 m, Tip: 0.02 m (or 0.00 m). With the default values, the hair looks like ropes in Cycles.
(Fibremesh, the 2nd button of Hair Net addon, are curves that are converted to mesh.)
Note:
The HairNet add-on 0.6.3 for Blender 2.9x has an issue at the moment. The generated hair sometimes moves down the Z-axis a little if you add more than one Particle System. You can fix this when you turn off the Particle System in the viewport (turn off the Monitor icon in the Particle System Settings). Or in Comb Mode, select all hair guides (Ctrl+A), and move them up again (G, Z, and use mouse).